Tensors via commutators
(2015) New trends in Hopf algebras and tensor categories — Location: Royal Flemish Academy of Belgium for Science and the Arts — Brussels (2.June.2015)
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- Abstract
- While the co-smash product of objects in a semi-abelian category may be used as a formal commutator [3, 2], after Carboni and Janelidze’s paper [1] it has also been clear that certain tensor products appear as co-smash products. This leads to an approach of tensor products via commutators. In my talk I will explain how the co-smash product of objects in the two- nilpotent core Nil2(X) of a semi-abelian category X determines a so-called bilinear product on the abelian core Ab(X) of X. In certain homological applications, this may then play the role of an intrinsic tensor product on X. (Joint work with Manfred Hartl.) References [1] A. Carboni and G. Janelidze, Smash product of pointed objects in lextensive categories, J. Pure Appl. Algebra 183 (2003), 27–43. [2] M. Hartl and B. Loiseau, On actions and strict actions in homological categories, Theory Appl. Categ. 27 (2013), no. 15, 347–392. [3] S. Mantovani and G. Metere, Normalities and commutators, J. Algebra 324 (2010), no. 9, 2568–2588.
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Van der Linden, T. (2015). Tensors via commutators. New trends in Hopf algebras and tensor categories, Royal Flemish Academy of Belgium for Science and the Arts — Brussels. https://hdl.handle.net/2078.5/59202